Answer to Question #299660 in Statistics and Probability for geeth

Question

The lifetime of an electrical component normally distributed with mean 800 hrs and standard deviation of 60 hrs.

What is the probability that the component will fail before 680hrs

If standard deviation remain 60 hrs what would have been the mean to ensure that not more than 10% of the components fail before 800hrs.

Answer 1

Let $X=$ lifetime of an electrical component: $X\sim N(\mu, \sigma^2).$

a. Given $\mu=800\ h, \sigma=60\ h.$

$$P(X<680)=P(Z<\dfrac{680-800}{60})$$

$$=P(Z<-2)\approx0.02275$$

b. Given $\sigma=60\ h.$

$$P(X>800)=0.1$$

$$P(Z>\dfrac{800-\mu}{60})=0.1$$

$$\dfrac{800-\mu}{60}\approx1.28155$$

$$\mu\approx723$$